From Robert L. Haun
Math Teachers problem.. Grades 12+

A pole 100 feet tall is erected next to a building 10' X 10' X 10' . Object is to cut off the pole so the upper end remains touching the part cut off, while the cut-off portion touches the cutoff point, the edge of the building and the ground. Note assume the pole is touching the building and is "very thin" What is/are the cutoff points??

We had a problem quite similar to this a while ago. In that case there was a particular choice of the variable that made the problem tractable. I think the same choice of variable might work in your situation also. See if you can modify the solution to that problem to suit your situation.